josiah takes a multiple - choice quiz that has three questions. each question has five answer options. if he…

josiah takes a multiple - choice quiz that has three questions. each question has five answer options. if he randomly chooses his answers, what is the probability that he will get all three correct?\n$\frac{1}{8}$\n$\frac{1}{25}$\n$\frac{1}{125}$\n$\frac{1}{243}$

josiah takes a multiple - choice quiz that has three questions. each question has five answer options. if he randomly chooses his answers, what is the probability that he will get all three correct?\n$\frac{1}{8}$\n$\frac{1}{25}$\n$\frac{1}{125}$\n$\frac{1}{243}$

Answer

Answer:

(\frac{1}{125})

Explanation:

Step1: Calculate the probability of getting one question correct

The probability of getting one question correct is (\frac{1}{5}) since there is 1 correct answer out of 5 options.

Step2: Use the multiplication rule for independent events

Since the questions are independent, the probability of getting all three correct is (\frac{1}{5}\times\frac{1}{5}\times\frac{1}{5}).

Step3: Calculate the product

[ \begin{align*} \frac{1}{5}\times\frac{1}{5}\times\frac{1}{5}&=\frac{1\times1\times1}{5\times5\times5}\ &=\frac{1}{125} \end{align*} ]